We can all agree that fighters like Jon Jones, Cain Valasquez, and Jose Aldo belong on the list in some form, but that agreement is still not built on anything directly measurable. The three’s many wins, and wins over various styles of fighting, surely give weight to the judgment that they belong in a top ten list, but the same could have been said about Barão before he had no answer to Dillashaw at UFC 173. Even though Barão had three dominant defenses as interim and undisputed champion (all pointing to a top pound-for-pound fighter), one data point served to change that entire judgment and to throw him off of the top-ten list.

The problem here is with the greater-than operator. There are logical problems to saying that a fighter is better than another fighter which aren’t captured in most discussions. Lists make assumptions like transitivity, which none of us should believe hold true in context of any fight. Fantasy matches within a weight class are difficult enough to think about because transitivity doesn’t hold. Pound-for-pound lists are worst than fantasy matches since at least fantasy matches doesn’t include some weird thought experiment about there being some factor that equalizes the difference between weight classes. At least if someone were to think about Valasquez v. Emelianko, he would be thinking about a potential bout between two people at the same weight class. Valesquez v. Aldo, though, involves some weird magic by which the weight disparity disappears, and the two meet on an equal footing.

In the end, that leaves top pound-for-pound lists an exercise in futility, built on something that quite isn’t there: the ability to measure fighter’s capabilities in a manner which make greater-than statements universally possible. What’s important about the pound-for-pound list is what isn’t being said and what is assumed to be common knowledge. There are arguments to be made at length about those fighters. A simple list assumes that everyone knows those arguments rather than bringing them to the forefront, and that is what should be done. Fighting is much too complex an art to allow for such lists to be made entirely validly. That doesn’t mean that we shouldn’t bother looking at them, it means that we should pay attention to the arguments in the background, and Barão going from sixth to under ten in Sherdog’s list shows why we should take them with more than just a grain of salt.